Finite Group Databasebeta

Q8×#88238 #16808441

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productQ8×#88238

Splittings

SylowC13 ⋊ Q8×#131

Subgroups

subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingD4×Q8×C13C4
prime radicalC2×#6129C23
cosocleC2×Dic13C25
hypercenterD4×Q8#261
hypocenterC13Q8×#131
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ D4×Q8

1882 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1115090);